Dear Gap Forum,
Vahid Dabbaghian asked
I want to get the character tables of the central extensions of group
PSL(3,4) but I don't know how I can define these extensions.
If only the character tables are needed and not the groups themselves
then most of this information is available in the GAP character table
The tables of the maximally cyclic central extensions are available
as `CharacterTable( "12_1.L3(4)" )' and `CharacterTable( "12_2.L3(4)" )',
and the table of the extension by a central group $2^2 \times 3$ is
available as `CharacterTable( "(2^2x3).L3(4)" )';
the ordering of classes and characters in these tables is compatible
with that in the ATLAS of Finite Groups.
The table of the Schur cover, which has the structure
$(4^2 \times 3).L_3(4)$, is currently not available in the GAP character
table library, but it would not be difficult to compute it from the
tables of the cyclic central extensions.